CN105531934B - The method and equipment used to perform the method for compression sensing for streaming data - Google Patents

Abstract

The present invention provides a kind of for sensing the computer implemented method of streaming data, it includes recursively sampling input traffic using overlapping windowing to be used to obtain subsequent measurement to obtain at least one baseline measurement about the input traffic, and by least one described baseline measurement.

Description

The method and used to perform the method for compression sensing for streaming data Equipment

Technical field

The present invention relates to a kind of method of compression sensing for streaming data and it is related to for executing the method Device.More specifically, some embodiments include: a method of the compression for streaming data senses, and uses The recursive algorithm of compression sensing is executed for convection type transmission data；With a kind of equipment or system or computer program product, The method for being able to carry out the compression sensing for streaming data.

Background technique

In field of signal processing, signal of interest can be by using several in the orthonormal basis suitably selected Coefficient sparsely indicates.Exemplarily, Fourier basis is used for piecewise continuous signals for frequency band constrained signal or wavelet basis, such as Image.Although a small amount of coefficient in corresponding base is enough to indicate these signals, Nyquist/Shannon sampling theorem shows to be at least Twice of sampling rate of the signal bandwidth.Such sampling rate is referred to as Nyquist rate in the art.In majority In the case of, indicated sampling rate is more much higher than enough numbers of coefficient.

Recently, for not according to the bandwidth of signal but according to its information content (that is, the number of the freedom degree of the signal Mesh) sampled signal and introduce compression sensing (CS) frame.This normal form for sampling shows compared in a certain given base In with rarefaction representation signal the lower sampling rate of classical sampling theory.It is natural in astronomy and biomedical imaging The type signal of generation is fitted this model.

Summary of the invention

The present invention proposes a kind of for sensing the computer-implemented side of streaming data according to one of embodiment Method comprising recursively sample input traffic using overlapping windowing to obtain at least one elder generation about the input traffic It preceding measured value and is used at least one described baseline measurement to obtain subsequent measurement.

A kind of system for sensing streaming data is proposed according to another embodiment of the present invention, and it includes multiple moulds Block, each module include the computer-readable media thereon with the computer executable instructions for following operation: using weight Recursively sampling input traffic obtains at least one baseline measurement about the input traffic for folded windowing, and by institute At least one baseline measurement is stated for obtaining subsequent measurement.

A kind of computer-readable storage medium is proposed according to still another embodiment of the invention, and record has for sensing stream thereon Formula transmits the computer program of data, and the computer program includes being able to use overlapping windowing recursively to sample input traffic To obtain about at least one baseline measurement of the input traffic and be used to obtain by least one described baseline measurement Obtain the algorithm of subsequent measurement.

According to another embodiment of the present invention, a kind of equipment for executing the compression sensing of streaming data is proposed, It includes being configured to recursively sample input traffic using overlapping windowing to obtain about the input traffic extremely The recurrence sampler of a few baseline measurement and the unit that at least one baseline measurement is used to obtain subsequent measurement.

According to one embodiment of present invention, the sensing of streaming data is the compression sensing of streaming data, and And recursive scheme is used to execute sampling by the method for sensing streaming data.At least one baseline measurement is used to obtain The step of obtaining subsequent measurement includes handling the input traffic sampled during recurrence sampling procedure via recursive estimation.

According to another embodiment of the present invention, method and apparatus proposed by the invention be related to about data flow about Previous estimated values obtain the input information of previous estimated values obtained during step, and the previous estimated values obtain step in institute Before stating recurrence sampling procedure.The method further includes based on the information obtained during data flow support detecting step It executes and counts estimation and calculated based on data obtained during the recursive estimation step for data flow support set Least-squares estimation (LSE) value.In addition, the method includes step of averaging according to another embodiment of the present invention, wherein It averages calculated least-squares estimation value, counting estimated value and the previous estimated values for calculating average value to be put down Mean value.The average value is used to obtain the new estimation value for streaming data.

It is according to still another embodiment of the invention, proposed by the present invention that the method further includes analyzing streaming data Compression sensing computation complexity and the step of estimate the degree of error of method for sensing streaming data.The method It further comprise that convergence is obtained in iteration optimization algorithms to decode new window, the acquisition step is opened including the use of the overlapping Overlaid windows structure used in window step and the signal estimated value about the previous window.The method still further comprises It averages to the signal estimated value obtained from multiple windows, execute the detection of support set and signal amplitude estimation.

It can also be according to the present invention using the Voting Scheme for carrying out firm support estimation in the presence of high measurement noise.

Detailed description of the invention

Understanding additional objects and advantages of the invention are described below by what is carried out from the included schema of combination, in the schema In:

Fig. 1 is according to an embodiment of the invention for sensing the block diagram of the method for streaming data；

Fig. 2 indicates the average handling time and ' simple method (naive for recurrence compression sensing in single time window apporach)'；

Fig. 3 indicates the result estimated using the support set of LASSO；

Fig. 4 indicate a) mean estimates, b) go inclined mean estimates and c) by voting and acquisition of averaging estimation The error curve diagram of value, and

Fig. 5 indicates the error curve diagram of ' decide by vote and average ' of average LASSO estimated value and convection type transmission data.

Specific embodiment

It is not carried out in a limiting sense to being described below for current best mode contemplated of the invention is practiced, but merely for It describes the purpose of General Principle of the invention and carries out.The scope of the present invention should be determined with reference to claims.

Although obtaining a large amount of progress in the field of compression sensing, does not discuss executed for convection type transmission data yet Compression sensing recursive algorithm.Not yet pass through discussion in the art borrow gradually open a window to inlet flow applied compression sense and from making an uproar The computation complexity and stability for the signal estimation that the sample of sound carries out.

As those skilled in the art will understand, aspect of the invention can be presented as system, method or computer program Product.Therefore, aspect of the invention can using complete hardware embodiment, complete software embodiment (comprising firmware, be resident it is soft Part, microcode etc.) or combination software and hardware in terms of embodiment (can all be collectively referred to as " circuit ", " module " herein or " be System ") form.In addition, aspect of the invention can take the form of computer program product, the computer program product embodies Record has in one or more computer-readable medias (that is, data storage medium) of computer readable program code thereon.

It can use any combination of one or more computer-readable medias.Computer-readable media can be computer Readable signal media or computer-readable storage medium.Computer-readable storage medium can be (such as, but not limited to) electronics, Magnetism, optics, electromagnetism, infrared ray or semiconductor system, device or any appropriate combination above-mentioned.It is computer-readable The more specific examples (non-exhaustive list) for storing media will include the following: portable computer magnetic sheet, is deposited hard disk at random Access to memory (RAM), read-only memory (ROM), Erasable Programmable Read Only Memory EPROM (EPROM or flash memory), optical fiber, Portable compact disc (CD-ROM), optical storage, magnetic storage device or aforementioned each any appropriate combination.At this In the content context of document, computer-readable storage medium (that is, data storage medium) can be held for that can contain or store by instruction Any tangible medium for the program that row system, device use or combination instruction execution system, device use.

Computer-readable signal medium may include the institute's propagation data signal for being wherein embodied with computer readable program code, For example, in a base band or as carrier wave a part.This transmitting signal any one of can take various forms, packet Containing (but being not limited to) electromagnetically, optics or its any appropriate combination.Computer-readable signal medium can be and non-computer can It reads storage media and can convey, propagate or transmit to refer to for being used or being combined by instruction execution system, device Any computer-readable media for the program for enabling execution system, device use.

Any appropriate media can be used (including but not limited to wireless, wired, optical fiber cable, RF etc. or above-mentioned any Appropriate combination) emit the program code embodied on computer-readable media.

The computer of the operation for executing aspect of the invention can be write with any combination of one or more programming languages Program code, one or more described programming languages are including, for example, the object-orienteds such as Java, Smalltalk, C++ or its fellow Programming language, and, for example, the conventional programs programming language such as " C " programming language or similar programming language.Said program code can All execute on the user's computer, part execute on the user's computer, as independent software package execute, partially with On the computer of family and part executes on the remote computer or all executes on a remote computer or server.Latter In situation, remote computer can be connected to user by any kind of network (including local area network (LAN) or wide area network (WAN)) Computer, or may be connected to outer computer (for example, by using internet of ISP).

It is said below with reference to the flow chart of the method for embodiment according to the present invention, equipment (system) and computer program product Bright and/or block diagram describes aspect of the invention.It will be understood that can by computer program instructions implementation flow chart illustrate and/ Or each frame in block diagram and flow chart illustrates and/or the combination of the frame in block diagram.These computer program instructions can be mentioned Be supplied to the processor of general purpose computer, special purpose computer or other programmable data processing devices with generate via computer or its The machine that the processor of its programmable data processing device executes, the machine creation for implement flow chart and/or one or The device for the function action specified in multiple block diagram blocks.

These computer program instructions may also be stored in computer-readable media and bootable computer, other programmable Data processing equipment or other devices work in a specific way.Computer program instructions can also be loaded into computer, Qi Take In programming data processing equipment or other devices, to cause to execute one on computer, other programmable devices or other devices Series of operative steps, to generate computer-implemented process, so that the instruction executed on computer or other programmable devices The process of function action for implementing to specify in flow chart and/or one or more block diagram blocks is provided.

In the following description, capitalization bold-faced letter mark matrix (for example, A), and black matrix lowercase indicates vector (example Such as, x).

Hereinafter, x_iFor indicating i-th of vector x, and a_iFor indicating the i-th column of matrix A.

I-th of sample vector (such as i-th window or the i-th sampling matrix of inlet flow) is by subscript (for example, x⁽ⁱ⁾Or A⁽ⁱ⁾) mark.

Inner product between two vectors a and b is denoted as

< a, b > :=a^Τb。

| S | the radix of instruction set S.

Ε_x[] indicated condition it is expected Ε_x[]=Ε [| x]

Compression sensing field in, be frequently used for characterization vector or matrix term be " k sparsity ", " mutual coherence ", " being limited equidistant property " and " general k sparse model ".Hereinafter, the term is briefly described to illustrate it in the document Intended meaning.

For vector x ∈ Rⁿ, support is defined as supp (x) :={ i:x_i≠0}。

For same vector x ∈ Rⁿ, pseudonorm l₀It is defined as | | x | |₀:=| supp (x) |, wherein x₀It is the support Radix.

If | | x | |₀≤ k and only exist | | x | |₀When≤k, vector x is only sparse.

Usual k < < n, n are the number of the column of matrix A.

Exemplarily, if x=[0 003 0-1 005 0], x ∈ R¹⁰、||x||₀=3, and x is 3 sparse 's.

For matrix A ∈ R^mxn, mutual coherence is defined as the maximum inner product between any two different lines of matrix A, such as Under:

For matrix, A ∈ R^mxn, and given 0 < k < n, if there is making the δ for meeting following formula_k∈ [0,1], then matrix A Equidistant property (RIP) is limited it is said that meeting:

This condition is for all x ∈ RⁿIt is answered for k sparse spike effectively, wherein δ_kIt needs sufficiently small.

Such as Gauss, Bernoulli, from be used as known to the random matrixes such as the randomly selected row of DFT matrix herein In for compress sensing matrix, this is because its with high probability meet be limited equidistant property.Meet the square for being limited equidistant property The example of battle array is:

A) the n random vector sampled from m N-dimension unit sphere,

B) m row random partial fourier matrix obtained is randomly choosed by equably tieing up Fourier matrix from n,

C) there is A_i,jThe random gaussian matrix of~N (0,1/m),

D) with the random Bernoulli matrix of equal probability, wherein

For most latter two situation, matrix A is to be greater than or equal toProbability meet any k≤c₁m/log(n/ K) defined δ_k, wherein c₁And c₂It is to be only dependent upon δ_kConstant.

The other terms used in the document are defined as follows:

" recursively " it is used to indicate and executes program and with self-similar manner duplicated project.In mathematics and computer science In, the method that the term refers to defined function, wherein the function of the definition is applied in the definition of its own.Specifically For, this defines the infinite number (functional value) of an example using limited expression, and examples a few for one, a example can be referred to other A example but its mode are so that may occur in which without circulation or unlimited reference chain.The term is also more generally for description with self similarity Mode repeats the process of purpose.Recurrence is that program is passed through when being related to calling described program itself one of the program the step of Process.It is referred to as " recursive " by recursive program.

In the signal processing, window function (also referred to as apodizing function or tapering function) is zero beyond a certain selected section Mathematical function.For example, be inside the section constant and be elsewhere zero function be referred to as rectangular window, this description Its figured shape.When another function or waveform/data sequence are multiplied by window function, product is also above the section Zero: left part be its overlapping part, i.e., " across the visual field of the window ".The application of window function includes frequency spectrum point Analysis, filter design and beam forming.In typical application, the window function used is non-negative smooth " bell " curve, but can Use rectangle, triangle and other functions.The more typically definition of window function does not need it in the same manner and is zero beyond section, only Wanting the window multiplied by the product of its variable parameter is square-integrable, also, more specifically, the function is sufficiently fast Fastly towards zero variation.When the length of data set to be converted is required greater than offer required frequency resolution institute, it is common practice to by it It is subdivided into compared with small set and individually makes its windowing.In order to mitigate " loss " at the window edge, individual set can be in due course Overlapping.

If x is linear vector x ∈ RⁿAnd y ∈ R^mIt is the vector of obtained sample, then

Y=Ax (1)

In A ∈ R^mxnIn the case where sampling (sensing) matrix, the present invention proposes method and apparatus to restore x in m < < n. It is to owe fixed linear system with the system that equation (1) indicates.According to compression sense, main result be if x be k it is sparse and k<c_m/ log (n/k), then being possible for the solution of this undetermined linear system.

Problem P described below should be solved₀To find out the most sparse spike x for generating measured value y.This problem is non-determined Property polynomial time difficult problem or NP difficult problem, this needs to search for all subsets of the column of A.From it is known in the art, if There are polynomial time for the reducible complete problem L of NP of H figure spirit (that is, L≤_TH) and and if only if being asked there are when described problem L Inscribing H is NP difficult problem.In other words, the prophesy machine (oracle with the prophesy for H can be passed through in polynomial time Machine) L is solved.

Problem P₀It is recited as

Ask | | x | |₀The minimum value Ax=y of major event

Due to problem P₀Generally NP difficult problem, so this problem must pass through method easy to control " approximation ".Two companies Continuous convex function optimization problem is used to restore sparse spike according to linear measurement.

First optimization problem is referred to as " base tracks (Basis Pursuit) ", wherein Solve problems P₀It is equivalent to and solves l₁ Minimization problem BP:

Ask | | x | |₁The minimum value Ax=y of major event

For all k sparse spike x, if A satisfaction is limited equidistant property (RIP), whereinIt is so aforementioned Problem is equivalent to P₀.Optimization problem (BP) is tracked referred to as base.It reruns, solves since (BP) can be used as linear program (BP) with solution generally for the large-scale intractable problem (P of example₀) comparison it is computationally more efficient, for example, via interior point method.

Optimization problem is referred to as least absolute value selection and shrinking percentage operator (Least Absolute Selection and Shrinkage Operator；LASSO).In the presence of noise, measurement model y=Ax becomes:

Y=Ax+w； (2)

Wherein w ∈ R^mIndicate that additivity measures noise.

In this setting, the variant that can be tracked using following base, i.e. base tracking denoising (BPDN), in statistical literature most It is referred to as LASSO well:

Ask | | x | |₁The minimum value of major event

Wherein properly selectTo explain the additive noise in measurement.

As known in the art, by duality, described problem can equally be mentioned with unrestricted optimization problem Out:

It minimizes

Wherein λ is the regularization parameter for controlling sparsity and rebuilding the equalization point between error.

It is about LASSO to the theorem useful for the recursive scheme of convection type transmission data execution compression sensing is generated The theorem of error, if statement A satisfaction is limited equidistant property (RIP), whereinSo solution x of equation (3)_* In accordance with formula:

WhereinIndicate model mispairing andIndicate noise.C₀And C₁It is constant, wherein x_kIt is arrow X is measured, wherein being set as 0 in addition to the institute of maximum k component is important.In other words, x_kIt is by remaining many k elements of x The vector obtained with highest magnitude.

Specifically, if x be k it is sparse andSo

Error is rebuild in the theorem statement has the upper limit delimited by following two item: first is attributed to model mistake The error matched, and second ratio for being and measuring noise variance.

Key is if m >=C_kLog (n/k), then by the matrix that is obtained from sampling from the random vector of unit sphere, Random gaussian matrix and random Bernoulli matrix meet the hypothesis to equidistant constant with high probability

Wherein C is the constant depending on each.

In the art, the error for illustrating LASSO can be used for nearly ideal support detection.In order to state nearly ideal support inspection The fruiting characteristic of survey defines general k sparse model.

If x ∈ RⁿIt indicates k sparse signal and Ix:=supp (x) is its support set, then believing in a case where Number x is purportedly to be generated by general k sparse model:

The support of x is uniformly selected at randomAnd | I_x|=k, and

Depending on Ix, non-zero symbol is equally likely to -1 and 1.

The support set of k sparse signal can be detected as follows:

Assuming that μ (A)≤c of constant c1₁N > 0 /log, then x is by general k sparse model and for constant c2'sIt generates.

If for Ix:=supp (x),

So pass through selection measured valueLASSO estimated value is obtained, wherein

W~N (0, σ²I)

It defers to:

Wherein i ∈ I_x

With at leastProbability.

For the sampling matrix with following element

A_i,j~N (0,1/m)

Operator norm is

Therefore the sparsity condition in the theorem becomes k≤c₁m/logn。

In order to meet this inequality, the value of m needs for m=c '₁k logn。

In addition, for random gaussian matrix

If m > O (log³N), then meeting the condition to coherence.

The boundary is combined, needs the m to be

m≥min{O(k logn),O(log³n)}。

Orthogonal matching pursuit (Orthogonal Matching Pursuit；It OMP is) for extensive according to noiseless measured value The greedy algorithm y=Ax of multiple sparse spike x.The algorithm iteratively selects and projecting to the linear span for having selected column The column of the residual error of approximation y are minimized to export the column subset of A.If illustrating the mutual relevant satisfaction of calculation matrix ASo OMP is measured according to noiseless restores k sparse signal.

It is by optimized close to algorithm institute for non-smooth Continuous Convex Function in the presence of the algorithm for LASSO exploitation Inspire: ISTA is close to gradient method, and FISTA is to accelerate close to gradient method, and SALSA is the substitution bootstrap technique of multiplier Application.

Since error is defined as G (x_t)-G(x_*), wherein G (x) is the objective function and x of the LASSO in equation (4)_* =arg minG (x), so 1/t of the error with 1/t, FISTA of ISTA²With the 1/t of SALSA²Decaying, wherein t is number of iterations Mesh.It is also known to the art that being used for the non-smooth optimized newton-type method of Continuous Convex Function, wherein rate of convergence is unlike 1=t² It is worse but be local secondary.

Signal of interest is infinite sequence { x_i}_{I=0,1 ...}, the case where as when handling streaming data.It is right In such signal of interest, the i-th window definition from stream transmission signal acquisition is

x⁽ⁱ⁾:=[x_ix_i+1...x_i+n-1]^T。

If x⁽ⁱ⁾Be known as it is sparse, then the above researching tool is suitable for restoring the signal section each window, because This is suitable for restoring data flow.However, the operating cost being related to is high, and efficiently online implementation is uncertain.

Therefore, according to the present invention it is proposed that a kind of method effectively sampled and restore streaming data.The method is to pass Return compression method for sensing, and hereafter will be described in detail the method.As will be further shown in detail in the document, this hair Bright the method shows low complex degree in sampling and estimating part, this makes its algorithm be suitable for efficient online implementation.

Wherein indicate { x_iIt is infinite sequence { x_i}_{I=0,1 ...}, and x⁽ⁱ⁾∈Rⁿ(the i-th window of length n).

It is with the R dynamic model expression inputted

The method described in the present invention allows the gradually measurement y using following form⁽ⁱ⁾Estimated value is providedConsolidate it is low multiple The design of miscellaneous degree sliding window algorithm

y⁽ⁱ⁾=A⁽ⁱ⁾x⁽ⁱ⁾ (7)

Wherein { A⁽ⁱ⁾It is measured value matrix sequence.If { x_iSparse enough (i.e. if for each in each window I, | | x⁽ⁱ⁾||₀≤ k, wherein k < < n) or if abiding by this condition with sufficiently high probability, consolidate low complex degree sliding window and calculate The design of method is possible.

If A⁽ⁱ⁾Meet and limits equidistant property, whereinThe method looked back in the document before so can Progressively it is applied to estimated value { x⁽ⁱ⁾}.Run the algorithm it is online be it is at high cost and it is therefore desirable for design in best situation It down can be qualifiedly as the dedicated substitution to such method.

According to the present invention, using the signal overlap between gradually window, by following recurrence sampling (coding step) and Recursive estimation (decoding step) composition:

About recurrence sampling procedure: in order to avoid the matrix multiple of every y (i), A (i) is designed so that y (i) can counted It calculates and is reused in y (i+1) with minimum of computation expense:

y⁽ⁱ⁺¹⁾=f (y⁽ⁱ⁾,x_i+n,x_i)。

About recursive estimation step: for the convergence of Accelerated iteration prioritization scheme, using the estimation for corresponding to previous window ValueTo deriveEstimation program starting point

Hereinafter, recurrence sampling procedure and recursive estimation step will be described in more detail.

About recurrence sampling procedure, the recurrence sampling plan with minimum of computation overhead features is proposed.In the first iteration, =0, previous estimated values are not present, therefore calculated be

y⁽⁰⁾=A⁽⁰⁾x⁽⁰⁾。

Recursively sense matrix A⁽ⁱ⁾Sequence it is chosen are as follows:

WhereinFor A⁽ⁱ⁾L column and P be permutation matrix:

Following lemma ensures the success of this encoding scheme: if A⁽⁰⁾Meet given k and constant δ_kIt is restricted equidistant Property, then A defined in equation (8) above⁽ⁱ⁾Also meet same k and δ_kRestricted equidistant property.

It follows equation (8) A⁽ⁱ⁾=A⁽⁰⁾Pⁱ, and by resetting A⁽⁰⁾Column obtain A⁽ⁱ⁾.According to definition, limitation The equidistant property of property is only dependent upon | | x | |₀, and for displacement (the equally A of the item of x⁽⁰⁾Column displacement) it is insensitive.

It is assumed that A⁽ⁱ⁾Specific recurrence select y⁽ⁱ⁺¹⁾It calculates as follows:

When signal of interest includes noise, the noisy measurement is labeled as

y⁽ⁱ⁾=b⁽ⁱ⁾+w⁽ⁱ⁾Wherein b⁽ⁱ⁾=A⁽ⁱ⁾x⁽ⁱ⁾

Therefore,

By by b⁽ⁱ⁺¹⁾Value substitute into be used for y⁽ⁱ⁺¹⁾Equation in, obtain:

By defining z⁽ⁱ⁾:=w⁽ⁱ⁾-w^(i-1)If { w⁽ⁱ⁾It is independent increasing process, then z⁽ⁱ⁾And z⁽ⁱ⁺¹⁾It is independent 's.

Sampling matrix { the A given in equation (8)⁽ⁱ⁾}_{I=0,1 ...}Specific selection meet the following conditions

A⁽ⁱ⁾x⁽ⁱ⁾=A⁽⁰⁾Pⁱx⁽ⁱ⁾

By by v⁽ⁱ⁾It is defined as v⁽ⁱ⁾:=P⁽ⁱ⁾x⁽ⁱ⁾, recurrence sampling be seen as by using same calculation matrix A⁽⁰⁾Come Encode v⁽ⁱ⁾.With the x given in equation (6)⁽ⁱ⁾Specific structure, removeOutside, v⁽ⁱ⁾And v^(i-1)All items it is equal.

For the recursive estimation of signal of interest, by utilizing estimated valueIt finds and is used forEstimated value.

In iterative algorithm, convergence rate depends on starting point to the distance of optimal solution.Accelerate convergence to realize, utilizes Overlapping and the following starting point of use between window:

Wherein j=2 ..., n-1'sIt is the part of the optimal solution based on previous window.This is claimed in optimization document Make ' thermal starting (warm start) '.By so selecting starting point, the expection number for being used for convergent iteration is reduced.It will be at this Actually show this situation in the part later of document, wherein specifically discussing quantitative result.

Hereinafter, the sparse signal of interest in given orthonormal basis is discussed.

Up to the present in the document for given n ∈ Z⁺It is implicitly assumed that from sequence { x_iObtain length n window x⁽ⁱ⁾Meet sparsity constraints | | x⁽ⁱ⁾||₀≤ k,In general, situation can be x⁽ⁱ⁾Itself is not sparse, but can suitably select It is sparsely indicated in the base selected.

x⁽ⁱ⁾∈RⁿDue to x⁽ⁱ⁾=Φ α⁽ⁱ⁾And it can sparsely be indicated in given orthonormal basis Φ, wherein α⁽ⁱ⁾It is sparse 's.

Assuming that the entire sequence { x on the window with size n_iCommon base, obtain:

y⁽ⁱ⁾=A⁽ⁱ⁾x⁽ⁱ⁾=A⁽ⁱ⁾Φα⁽ⁱ⁾。

For the compression to be carried out sensing estimation, A⁽ⁱ⁾Φ, which needs to meet, is limited equidistant property.For random matrix A⁽ⁱ⁾With The product of any fixed matrix is limited equidistant property with high probability satisfaction.In the case, in sparsity base α⁽ⁱ⁾Middle recovery letter Number LASSO problem expression are as follows:

It asksMinimum value

Wherein pass through x⁽ⁱ⁾=Φ α⁽ⁱ⁾Given input signal.

How the problem of demand solution is based on α⁽ⁱ⁾It finds for α⁽ⁱ⁺¹⁾Recurrence update with have in recursive estimation The convergent good initial estimate of acceleration, such as E [α⁽ⁱ⁺¹⁾|α⁽ⁱ⁾]。

It is obtained using equation (6):

Wherein 0_n-1It is the vector with length n-1 that all elements are set as to 0.

Because of x⁽ⁱ⁾=Φ α⁽ⁱ⁾, it obtains:

With

Formerly make two sides multiplied by Ψ=Φ in the formula of front^-1, it follows:

Wherein Π :=P^TIt is the permutation matrix given in equation (9), and

It is the first row and last line of orthonormal basis Φ respectively.

Derive that efficient update rule, Fourier basis are concerned Φ since the base can be directed to.For Fourier The recurrence sampling of phyllopodium is as follows:

If Φ is n × n inverse discrete Fourier transform (IDFT) matrix with following item

WhereinIn the case:

Wherein Ω_nIt is n × n diagonal matrix, wherein (Ω_n)_i,i=ω^-(i-1), and Ψ=Φ^-1It is normal orthogonal Fu Vertical phyllopodium.

In that particular case, equation (11) is simplified to equation (12), this is because the ring shift of time domain is corresponding Being multiplied in Fourier domain with complex exponential, such as Ψ ∏=Ω_nΨ and Ψ Φ=I.

As seen from the above, although being in general based on α⁽ⁱ⁾Calculate α⁽ⁱ⁺¹⁾The number of calculating be O (n²), but for Fourier Phyllopodium is O (n), this is because multiplied by α⁽ⁱ⁾Matrix be diagonal matrix.

As previously shown, in the presence of noise, by E [α in iteration LASSO solver⁽ⁱ⁺¹⁾|α⁽ⁱ⁾] estimated value use Make starting point to accelerate convergence to realize for thermal starting.

A kind of mode for improveing error variance is by averaging to the estimated value obtained from gradually window.Use estimation ValueMean estimatesDefined i-th for being used to transmit as a stream signal, i.e. x_i, such as:

Wherein average to i+1 many estimated values of the n of i>=n-1 many estimated values and i<n-1.

I >=n-1 is considered for simplicity, is further obtained:

Wherein (a) is by being applied to x²Jensen inequality infer.The inequality implies that rebuilding error can only pass through It is averaged to estimated value to reduce.

Hereinafter, the expected l for rebuilding error is analyzed by curved-edge polygons formula and using following formula₂Norm

Wherein j ≠ k.

The case where the case where in order to count convenience, consider i>=n-1, i<n-1 is similar.

Gained equation is the so-called deviation variation decomposition of estimator.It can be seen that Section 2 is close as length of window increases Zero and rebuild square that error progressively converges the deviation of LASSO.

Hereinafter, algorithm discussion proposed according to the present invention.

In general, minimum absolutely selection is with shrinking percentage operator (LASSO) in its mapping R^m→RⁿWhen generate count biasing estimate Gauge, wherein m≤n.If utilizing the overlapping between window by directly averaging to LASSO estimated value, rebuild Structure error is attributed to deviation and and is not up to zero.On the other hand, least-squares estimation (LSE) is not biasing for overdetermined system Estimator；As above described in the document, LASSO can be used for estimating the support set of signal, and LSE then can be applied and the collection It closes.Based on these observations, the Two-step estimation program that evaluated error is reduced for restoring sampled signal is proposed.It obtains first LASSO estimated valueIt is then used as to the input for removing inclined algorithm.In order to go to hold partially to the support set of LASSO estimated value Row LSE is to obtainIts | | x⁽ⁱ⁾||₀The actual non-zero of signal is provided when≤m and correctly identification support does not bias estimation Device.Then, inclined estimated value is gone to average to what is obtained on gradually window.The block diagram of method and the pseudo-code of algorithm can be shown in respectively In algorithm 1 in attached drawing and hereafter.

1 recurrence of algorithm compression sensing:

Input: A⁽⁰⁾∈R^mxn,{x},λ≥0

Output: estimated value

Block diagram according to an embodiment of the invention for sensing the method for streaming data indicates in Fig. 1. Method according to this embodiment includes sampling input traffic recursively using overlapping casing milling steps to obtain at least one elder generation Preceding measured value and the baseline measurement is used for the step of obtaining subsequent measurement.More accurately, the method includes recurrence Sample the step 102 of input traffic.The number sampled during recurrence sampling procedure 102 is handled via recursive estimation step 104 According to.Input obtains during the previous estimated values before recurrence sampling obtain step 116 also during recursive estimation step 104 Information about previous estimated values.As described by the step 6 above in association with recurrence Sampling Method, in 106 phase of support detecting step Between utilize the data that obtain during recursive estimation step 104.The information handled due to support detecting step can be used for counting Number estimation, as Fig. 1 step 110 in institute show and corresponding to recurrence Sampling Method step 7.Such as sampled above in association with recurrence Described by the step 8 of algorithm, utilize the information obtained in step 106 during the step 108 that LSE is calculated support set. Then, as described by the step 9 above in association with recurrence Sampling Method, the LSE of support set and estimation are counted in step 112 It averages.According to an embodiment of the method, also in step 112 to the previous estimated values obtained during step 116 It averages.As described by the step 10 above in association with recurrence Sampling Method, new estimation value is obtained in step 114.

The computation complexity and evaluated error of the method can also be analyzed according to the method for such embodiment.

More accurately, hereinafter, the complexity and error variance of the method are analyzed, and introduces and is used for more firm branch Collect the voting algorithm of detection.

Indicate that the block diagram of Fig. 1 of one embodiment of the method is extended to including the variable overlapping between gradually window Method.

What is considered is the generalization that sensing is wherein executed via the recurrence windowing with 0 < τ≤n overlapping.

If A ∈ R^mxnInstruction sampling matrix, then i indication window index, and η_iFor sampling efficiency, i.e., until the time (n+i) ratio of the number of acquired total sample and sensed item until.For a window, sampling efficiency m/n, this is Because sampling matrix is A ∈ R^mxn。

When to the i-th window knot, n+ (i-1) is restored when having obtained im sample_τA element.Progressive sampling efficiency are as follows:

If being substituted for organizing the coding in the en coding that τ updates using row (that is, sampling square by using by ring shift Battle array τ time matrix obtained), then progressive sampling efficiency becomes:

In the latter case, recurrence sampling method is progressively equivalent to each time example and obtains a sample.It is described Method has an advantage that noise suppressed.By obtaining overlaid windows, with the smallestNumber senses each element, therefore It can be used for improving accuracy of estimation using multiple cooperation decodings.

The application that LASSO estimates to signal support is previously discussed in the document.Further in the document, benefit is introduced With the method for the estimation support on the gradually window for the more firm support detection in high measurement noise.Signal amplitude simultaneously When the non-sufficiently high noise to be subjected to the noise level or more, aforementioned support testing mechanism can miss non-zero position (failing to report) or Detect wrong support (false positive).Therefore, the support detection theorem previously discussed in the document can be used smaller regularization normal Number λ detect the support of lower minimum non-zero value to reduce the probability of success as cost.Assuming that false positive is randomly distributed on all i Set { 0 ..., n-1 } supp (x⁽ⁱ⁾) on, the threshold value for needing to be detected as the minimum number of support by introducing position can The false positive to noise system is reduced in low signal.

By introducing ' voting machine ', the Double Step algorithm obtained in voting can indicate the support detection block in Fig. 1 In 106.The Double Step algorithm is worked by solving LASSO as follows

If by ξ₁It is set as > 0, then findingAbsolute value be greater than ξ₁Index estimate x⁽ⁱ⁾Support；I-th In window

Sequence definition containing ballot paper is { ν_i, and the index i number for being used for least-squares estimation (LSE) is defined as {L₁}.In the beginning of algorithm, by { ν_iAnd { L₁It is set as zero.The ballot paper on the position for each window, in set Through being added conductIt is described set byIt indicates, wherein subscriptFor the index in window to be turned Change the overall index on streaming data into.By to ballot paper { ν_iNumber threshold application ξ₂∈Z⁺, find enough Secondary voting is subjected to the index for non-zero and stores it in

In.

Select threshold xi₂So thatTherefore the overdetermined system for being used for LSE is generated.It is solved based on these indexes super Determine least square problem,

WhereinIt is by extracting by gatheringThe A of index⁽ⁱ⁾Column matrix obtained.Then in order to execute to most Small two, which multiply estimated value, averages, and recycling number is directed to incremental as follows for the entry in LSE program

Vector?In, and vector x' ∈ RⁿIt is by will be byThe element of index is set to least square and estimates Evaluation is (such as) and all other index is set to 0 to generate.Then mean estimates is updated as follows:

Hereinafter analyze the estimation error variance and computation complexity of the method according to one embodiment.

Before carrying out the analysis to the estimation error variance of two step RCS methods, following lemma is introduced:

Lemma 5.1: byIt is indicated in the solution in equation (4) to LASSO, byIndicate its support collection It closes, and passes throughThe least square solution is limited to column A_I

Meet following equation:

Independently of selected support, the following is suitable for applying LASSO in the support of LASSO estimated value to estimate and most Small two multiply:

WhereinThe optimality condition of LASSO obtains:

Wherein sgn (v) is the sign function for expanding to vector.Normal equation is pronounced

Therefore:

Wherein (a) is inferred by equation (15) and normal equation, (b) is inferred from the following

And

And (c) fromInfer.

If it is assumed that noise is uncorrelated to support detection, that is,

Wherein wherein Ai indicates support detection successful event in the i-th window to i ≠ j,

Following theorem provides the upper limit to the reconstruction error variance of the Double Step algorithm proposed.

According to the theorem about the error variance for proposed algorithm, discussed condition is being detected above in association with support Down and assuming that noise is in the incoherent situation of support detection for fixing k and n, the following conditions are effective:

Wherein

And

P(A^c)=1-P (A).

In order to prove the validity of theorem described above, need to meet following three conditions:

First condition are as follows:

M and k is given, wherein k≤m, for mxk matrix A (wherein A_{I, j}~N (0,1/m)), singular value

s₁(A)≥...≥s_k(A) meet condition:

Second condition are as follows:

By consistent boundary,

It is defined as Lasso estimated value.It is by applying the support in LassoOn least square obtain.

Define LASSO estimated valueAnd as follows by applying in LASSO supportOn least square estimated Value:

Wherein

In event of the support through correctly detecting in all n connected windows,

A₁∩…∩A_n, common least-squares estimation value is

MatrixIt is reversible, this is becauseSingular value be non-zero probability it is high.

According to standard LSE,

To any fixterm of the first item of the n times estimation in then signal, such as v_n-1=x_n-1, give

M~k log (n/k)

This value of m is almost reduced with 1/n, therefore is rebuild variance and detected the successful feelings in n connected windows in support Reach zero under condition.

In third time, it is important that understand the supplement to previous occasion,

ForWithThe above lemma obtains:

Therefore:

Using triangle inequality, the `2 norm of the difference between the LSE estimated value and actual signal to support set is obtained The upper limit:

It is obtained by combining these results:

By substituting into inequality 17, usingWithProbability and pay attention to v,WithCan respectively with x,WithIt exchanges To obtain above equation.

Analysis recursion is hereinafter compressed to the computation complexity of sensing algorithm.

If i is widow index, A⁽ⁱ⁾∈R^mxnIt is sampling matrix, and step is slided in τ instruction, then in the i-th window n+ (i-1) number of the sliding groove between gradually window has been restored at the end of τ.

Pass through A⁽⁰⁾ _x ⁽⁰⁾Sample first window.This needs O (mn) basic operation, such as mutually adduction is multiplied.In home window Later, window

x⁽ⁱ⁾=[x_iτx_iτ+1…x_iτ+n-1]

Sampling by complexity be organizing the recurrence sampling that τ updates with row and realizing for O (m τ).Therefore in the i-th window At the end of, total complexity of sampling is O (mn)+O (mt) i, and wherein the average complexity of recurrence sampling is O (m τ).

Iterative solution device is derived to other contributions of computation complexity.It is expected that complexity, which is attributed to the fact that, can be calculated as each change Operation number in generation is multiplied by the expected numbers purpose iterative solution device in convergent iteration.Although the former depends on specific calculation Method, but the latter is function of the starting point at a distance from optimal solution, is limited to the case where using recursive estimation as follows:

It uses:

As starting point, obtain:

The validity of statement made above is proved as follows:

It obtains norm and is obtained using triangle inequality:

In the case where checking the theorem for providing Lasso error, obtain:

The accurate computation complexity of each iteration depends on the algorithm.Minimally, the iterative solution for LASSO Device needs that sampling matrix is multiplied with estimated value at the iteration for needing O (mn) to operate.It declines in cost function sublinear Subtract (for example, 1/t²) algorithm in, such as in FISTA, obtainSo thatRequired iteration number

(x* is optimal solution), withProportional, wherein x [0] is the starting point of the algorithm.It is limited according to this, It can be seen that the average of iteration is proportional to the Euclidean distance of the starting point of algorithm and optimum point.

For sequence { x1 } i=0,1 ..., wherein for all iWith(wherein C > 0) It is constant, the expection number of the convergent iteration of the algorithm for wherein decaying to cost function sublinear is for muting MeasurementNoise is measured with for i.i.d.

It is set forth above true, this is because: due to x⁽ⁱ⁾It is k sparse, so the item

WithDeclined according to equation 18.

Pass through | x_i|≤C is obtained

For noisy measurement, itemIt is related with noise level.Since noise is with high probability With distribution N (0, σ²I it), therefore by the condition that the theorem proposes limitsPay close attention to the error of LASSO.User Formula (18) time as a result, discovery iteration expection number be in the presence of noise

In the above analysis, average complexity is O (m τ) for recurrence sampling, and for optimization algorithm (minimally) It is O (mn).In order to restore each component of inlet flow without omitting element, τ≤n, consequently found that the complexity of iteration optimization is excellent In average complexity.

By using condition m >=Ck log (n/k) of the random vector for being sampled from unit sphere, random gaussian matrix Meet condition with random Bernoulli matrixThe following table 1 shows that the average computation of the various sparsity classifications of k is multiple Miscellaneous degree.

Experimental result

It is generated according to stochastic model for the data in simulating:

Wherein unless otherwise stated, otherwise p=0.05.

Measurement model is

y⁽ⁱ⁾=A⁽ⁱ⁾x⁽ⁱ⁾+w⁽ⁱ⁾

Wherein w⁽ⁱ⁾~N (0, σ²I)

Wherein σ > 0

And it samples matrix and is

A⁽⁰⁾∈R^mxn

Wherein m is 6 times of expected numbers purpose of the nonzero term in a window, that is, m=6pn, and wherein n is equal to window Length.

Experimentally shown by RCS by comparing using FISTA, for solving the acceleration of LASSO close to gradient side The speed gain that average time needed for estimating given window when method is realized.Compare RCS and so-called ' simple method ', wherein leading to The matrix multiple crossed in each window is sampled, and the FISTA since full zero vector.It shows in Fig. 2 in different situations Average time needed for one window of lower recovery.As that can observe in Fig. 2, the average handling time for RCS is lower than it The processing time needed for its method.

The experimental result carried out using LASSO to support estimation is discussed again.In measurement x ∈ R⁶⁰⁰⁰In, | | x | |₀=60, A ∈R^mx6000By with A_i,jThe Gaussian Profile of~N (0,1/m) generates, and w has σ=0.1.As proposed by LASSO theorem, For these parameters, useSolve LASSO

And by sampling from U ([- 3.34, -4:34] U [3.34,4.34]), the non-zero magnitude of x meets

In simulations, acquired number of samples changes with signal m, and is equal to │ by using verification and measurement ratio and detects branch The collection practical support of ∩ compare the practical support │ of │/│ and false positive rate=detected support of │ the practical practical support │ of support │/│ grind Study carefully support estimation accuracy, wherein │ │ indicate cardinality of a set and be esodisparity operator.It should be noted that fixed for this Justice, false positive rate can be greater than one.

Compare two methods for support detection.First method is by solving LASSO and obtaining the conduct of non-zero position Support, and second method is the position for being greater than threshold value by obtaining the absolute magnitude of estimated value.Fig. 3 shows the gained of two methods Curve is averaging as the 20 generation input signals of each value and the verification and measurement ratio to obtained by and false positive for being randomly directed to m It is worth and obtains.It, can be by suitably adjusting such as from the schema as it can be seen that although property of the verification and measurement ratio in two methods is similar The threshold value of gained LASSO estimated value significantly reduces false positive.

Illustrate in Fig. 3 and estimated using the support set of LASSO: wherein n=6000, σ=0.1, min | x_i|≥ 3.34 threshold xi₁=0.01,0.10 and 1.00.Circular mark describes verification and measurement ratio, and square indicia describes false positive rate.

It is discussed in detail Ru above, LASSO method can be used together to generate with least-squares estimation with voting strategy Estimator is not biased.Fig. 4 show a) single LASSO estimated value, b) mean estimates, c) voting strategy and d) go partially with averaging The comparison of the execution of value.

By using fixed x ∈ RⁿAnd it is measured with uncorrelated noise to obtain the schema.It can See that the error of mean estimates is not reduced to zero, it is bias estimator that this, which is attributed to LASSO, as previously solved in the document It releases.Specifically, Fig. 4 be a) mean estimates, b) go partially with mean estimates and c) by voting and acquisition of averaging Estimated value error curve diagram expression.

Referring now to Figure 5, the schema illustrates that average LASSO estimated value and convection type transmit ' deciding by vote and ask flat for data Mean value ' error curve diagram.

Fig. 5 is shown to be obtained using ' decide by vote and average ' algorithm of average LASSO estimated value and convection type transmission data The comparison between window reconstruction structure error obtained.Data are randomly generated, wherein select an item as support, p=0.05, and And its amplitude is distributed independently rendered and identically as homogeneous distribution

U([-1.3847,-2.3847]∪[1.3847,2.3847])

To meet the condition of support detection theorem, wherein n=400, m=5np=100, and sampling matrix is Gaussian Moment Battle array.Measurement is by w⁽ⁱ⁾~N (0, σ²I_m) influence,

Wherein σ=0.05, and voting algorithm uses ξ₁=0.5 and ξ₂=20.It is attributed to as can be seen, voting provides displaying It waits and collects ξ₂The reconstruction error of the jump of ballot paper, to use item in LSE.However, being also shown, it is being subjected to the position After the part of support, error drops at once than low value of only averaging to LASSO estimated value.

Therefore, according to one embodiment propose it is a kind of for about convection type transmission data compression sensing recurrence sampling and The high efficiency method of Iterative restoration.The method obtains the estimated value of signal more using the signal overlap gradually handled between window Rapid convergence speed, while realizing that estimate variance reduces in the presence of noise.

In addition, propose according to another embodiment Two-step estimation program come based on LASSO make signal not bias estimator close Seemingly, support detection a) wherein is executed by solving LASSO, and b) is obtained by solving common least square to estimation support set Obtain signal estimation.The computation complexity of algorithm is O (mn), and wherein m is the number of acquired sample and n is length of window.It is logical Cross the experiment displaying convergence time for being suitable for the online implementation on streaming data.

Therefore, to sum up, embodiment includes a kind of method of compression sensing for streaming data, it is related to holding Row executes the recursive scheme of compression sensing for convection type transmission data, and the scheme is capable of the calculating of good analysis the method Complexity and evaluated error.According to one embodiment, surveyed simultaneously when obtaining next measured value using previous via overlapping windowing Magnitude recursively samples input traffic.Using overlaid windows structure, using the signal estimated value from previous window, so as to More rapid convergence is realized in iteration optimization algorithms to decode new window.By asking flat to the signal estimated value obtained from multiple windows Mean value enhances accuracy of estimation.In order to remove the biasing of estimator, Two-step estimation program is proposed according to one embodiment, including The detection of support set and signal amplitude estimation.In addition, one embodiment includes steady for carrying out in the presence of high measurement noise The Voting Scheme of clamped collection estimation.

Using the simulation knot obtained when compressing the device sensed for streaming data according to one embodiment Fruit shows relative to the ten times of acceleration sensed to data stream application conventional compression, while having to signal amplitude and noise level Significantly lower reconstruction error is obtained in the case where less condition.

According to another embodiment, it is also proposed that for sensing the device of streaming data.Number is transmitted as a stream for sensing According to described device include device for recursively sampling input traffic and for baseline measurement to be used to obtain it is subsequent The device of measured value.Device for recursively sampling input traffic is able to use overlapping casing milling steps to obtain at least one Baseline measurement.

One embodiment includes to carry out ranging for ultra-broadband signal.For example, device can constantly monitor periodically to send out Penetrate the return pulse of spike (signal of the transmitting is periodic).In general, device receives prominent echo plus additional Multiple echoes.If device be it is mobile, prominent echo only slightly changes to another period from a cycle, such as multiple times Wave is the same.This and non-periodic signals, and only approximately periodic signal, and sliding window algorithm will track these naturally Shift echo.In such embodiments, the echo data for carrying out this sonic sensor is thereby converted into range data.

It in another example, can be according to method and system converting biological medicine sample data as described above.Citing comes It says, can be configured to certainly from people for rebuilding the embodiment of electrocardiogram or EEG signal to handle according to disclosed herein Body receives the sample of one or more electric transducers of electric signal.In some embodiments, reconstructed structure signal can be with one or more Diagnose the label characteristics match of illness.

In another example, it can handle as described herein from camera, photoelectricity or other pixel array sensor (examples Such as, be configured to receive visible or infrared light) sample data.For example, using these technologies, a kind of equipment can It improves power efficiency or improves effective susceptibility of sensor.

In other embodiments, the environmental sensor number such as temperature, wind speed, wind direction precipitation can be handled as described herein According to.

Implementable the device of the invention is software device, hardware device or combinations thereof.

System described above and method, which can embody, (for example) in radio modem or integrates such modulation /demodulation In the wireless device of device.

It should be understood that depending on embodiment, some action or event of any one of method described herein can Executed, can be added, merged, or omitted altogether with different order (for example, practice the method do not need it is all described dynamic Work or event).In addition, in certain embodiments, can for example via multiple threads, interrupt processing or multiple processors simultaneously and Non- sequentially execution movement or event.

Those skilled in the art will realize that the various theorys described in conjunction with methods disclosed herein, system and equipment Bright property logical block, module, circuit and algorithm steps are implementable for electronic hardware, the computer software or two executed by processor The combination of person.It is above substantially its functionality to be described to various theorys for this interchangeability for clearly demonstrating hardware and software Bright property component, block, module, circuit and step.This functionality is implemented as hardware or software depends on specific application and applies The design constraint being added in whole system.Those skilled in the art is implemented in different ways for each specific application Described function, but the decision of such embodiment should not be interpreted as causing a departure from the scope of the present.

In addition, embodiment disclosed herein available electron device or circuit are practiced or carried out, the electronic device or circuit Such as general processor, digital signal processor (DSP), specific integrated circuit (ASIC), field programmable gate array (FPGA) Or it is designed to execute other programmable logic devices, discrete gate or the transistor logic, discrete of function described herein Hardware component, or any combination thereof.General processor can be microprocessor, but in alternative solution, and processor, which can be, appoints What conventional processors, controller, microcontroller or state machine.Processor also is embodied as the combination of computing device, for example, DSP Combination, multi-microprocessor with microprocessor, in conjunction with one or more microprocessors of DSP core or any other this configuration.

The step of method or algorithm for being described in conjunction with embodiment disclosed herein can be embodied directly in hardware, by It manages in the software module or the combination of both that device executes.Software module may reside within RAM memory, flash memory, ROM In memory, eprom memory, eeprom memory, register, hard disk, moveable magnetic disc, CD-ROM or technique In the storage media for any other form known.Exemplary storage medium is couple to processor, and this kind of processor can be from storage matchmaker Body reads information, and writes information into storage media.In alternative solution, stores media and processor is integral.Processing Device and storage media can reside in ASIC.ASIC can reside in user terminal.In alternative solution, processor and storage matchmaker It is resident in the user terminal that body can be used as discrete component.

Specifically, according to an embodiment of the invention, a kind of equipment for executing the compression sensing of streaming data Include: be configured to using overlapping windowing recursively sampling input traffic come obtain about input traffic at least one The recurrence sampler of baseline measurement, and at least one baseline measurement is used to obtain the unit of subsequent measurement.

The equipment proposed according to one embodiment of present invention includes the recurrence based on the recursive scheme for executing sensing Sampler.The equipment of compression sensing for executing streaming data of the invention further includes for handling via recursive estimation The processing unit of the input traffic sampled during recurrence sampling procedure.

According to the present invention, the equipment for executing the compression sensing of streaming data further includes for transmitting about first Preceding estimated value obtains the storage device of the input information of the data flow of the previous estimated values obtained during step.In addition, of the invention The equipment of the compression sensing for executing streaming data include being configured to based in data flow support detecting step Period, information obtained executed the counter for counting estimation.Further, equipment of the invention may also include for being based on Data obtained calculate least-squares estimation (LSE) value for data flow support set during the recursive estimation step Calculator.The equipment proposed according to one embodiment of present invention further includes for the least-squares estimation value to calculating, counting Estimated value and previous estimated values average to calculate average value to obtain the processing unit of average value.It is also envisioned that according to the present invention The equipment of proposition includes the estimator for the degree of error for estimating to sense the method for streaming data.In addition, the present invention proposes Equipment may also include the processing unit for averaging to the signal estimated value obtained from multiple windows.

Describe various examples.These and other example is in the scope of the following claims.

Claims (27)

1. a kind of method for executing the compression sensing of streaming data comprising:

Input traffic is recursively sampled at least partially by the following gradually overlaid windows that operates with:

Recursively sequence of the selection for the sensing matrix A of the overlaid windows in the input traffic, the sensing square The sequence of battle array A includes initial sensing matrix A⁽⁰⁾, sensing matrix A⁽ⁱ⁾With sensing matrix A⁽ⁱ⁺¹⁾, the institute of (i+2) a overlaid windows State sensing matrix A⁽ⁱ⁺¹⁾It is defined by following equation: A⁽ⁱ⁺¹⁾=[a₂ ⁽ⁱ⁾,a₃ ⁽ⁱ⁾,...,a_n ⁽ⁱ⁾,a_l ⁽ⁱ⁾], wherein a₁ ⁽ⁱ⁾、a₂ ⁽ⁱ⁾、a₃ ⁽ⁱ⁾... and a_n ⁽ⁱ⁾The respectively described sensing matrix A⁽ⁱ⁾The 1st, 2,3 ... and n arrange, n is the length of each overlaid windows, and i is big In or equal to 0；And

The measured value y for being used for (i+2) a overlaid windows is obtained using following equation⁽ⁱ⁺¹⁾: y⁽ⁱ⁺¹⁾=y⁽ⁱ⁾+(x_i+n- x_i)a_l ⁽ⁱ⁾, wherein i is greater than or equal to 0, and corresponds to the signal x of the input traffic of (i+1) a overlaid windows⁽ⁱ⁾ It is defined by following equation: x⁽ⁱ⁾=[x_ix_i+1...x_i+n-1]^T, and it is used for the measured value y of initial overlaid windows⁽⁰⁾By with lower section Formula definition: y⁽⁰⁾=A⁽⁰⁾x⁽⁰⁾。

2. the method according to claim 1 for executing the compression sensing of streaming data, wherein obtaining the survey Magnitude y⁽ⁱ⁺¹⁾The step of do not executing the matrix multiple for any one of sequence sensing matrix for being related to the sensing matrix A In the case of execute.

3. the method according to claim 1 for executing the compression sensing of streaming data, wherein obtaining the survey Magnitude y⁽ⁱ⁺¹⁾The step of include handling the input data that is sampled during the recurrence sampling procedure via recursive estimation Stream.

4. the method according to claim 3 for executing the compression sensing of streaming data, further comprising:

The information about the input traffic is received, wherein the information is obtained about during previous estimated values obtain step The previous estimated values obtained execute the previous estimated values before the recurrence sampling procedure and obtain step.

5. the method according to claim 3 for executing the compression sensing of streaming data, further comprising:

Detection data stream support, and

It is executed based on information obtained during the data flow support detecting step and counts estimation.

6. the method according to claim 3 for executing the compression sensing of streaming data, further comprises base The least-squares estimation LSE value for being used for data flow support set is calculated in data obtained during recursive estimation step.

7. the method according to claim 6 for executing the compression sensing of streaming data, further comprises meter The average value of the least-squares estimation value, counting estimated value and previous estimated values that are computed.

8. the method according to claim 7 for executing the compression sensing of streaming data, further comprises making The new estimation value for the streaming data is obtained with the average value.

9. the method according to claim 1 for executing the compression sensing of streaming data, further comprises point Analyse the computation complexity of the compression sensing of streaming data.

10. the method according to claim 9 for executing the compression sensing of streaming data, further comprises estimating Count the degree of error for sensing the method for streaming data.

11. the method according to claim 1 for executing the compression sensing of streaming data, wherein it is described recursively Sampling includes obtaining convergence in the iteration optimization algorithms to overlaid windows to decode new window.

12. the method according to claim 11 for executing the compression sensing of streaming data, wherein the acquisition Step is including the use of the overlaid windows structure as used in the step for using gradually overlaid windows and about previous overlapping window The signal estimated value of mouth.

13. the method according to claim 1 for executing the compression sensing of streaming data, further comprises pair The signal estimated value obtained from the gradually overlaid windows is averaged.

14. the method according to claim 13 for executing the compression sensing of streaming data, further comprising:

The detection of support set is executed, and

Signal amplitude estimation.

15. the method according to claim 1 for executing the compression sensing of streaming data, further comprises answering With the Voting Scheme for carrying out firm support estimation in the presence of high measurement value noise.

16. a kind of system for executing the compression sensing of streaming data, it includes multiple modules, each module includes it The upper computer-readable media with the computer executable instructions for following operation:

Input traffic is recursively sampled at least partially by the following gradually overlaid windows that operates with:

Recursively sequence of the selection for the sensing matrix A of the overlaid windows in the input traffic, the sensing square The sequence of battle array A includes initial sensing matrix A⁽⁰⁾, sensing matrix A⁽ⁱ⁾With sensing matrix A⁽ⁱ⁺¹⁾, the institute of (i+2) a overlaid windows State sensing matrix A⁽ⁱ⁺¹⁾It is defined by following equation: A⁽ⁱ⁺¹⁾=[a₂ ⁽ⁱ⁾,a₃ ⁽ⁱ⁾,...,a_n ⁽ⁱ⁾,a_l ⁽ⁱ⁾], wherein a₁ ⁽ⁱ⁾、a₂ ⁽ⁱ⁾、a₃ ⁽ⁱ⁾... and a_n ⁽ⁱ⁾The respectively described sensing matrix A⁽ⁱ⁾The 1st, 2,3 ... and n arrange, n is the length of each overlaid windows, and i is big In or equal to 0；And

The measured value y for being used for (i+2) a overlaid windows is obtained using following equation⁽ⁱ⁺¹⁾: y⁽ⁱ⁺¹⁾=y⁽ⁱ⁾+(x_i+n- x_i)a_l ⁽ⁱ⁾, wherein i is greater than or equal to 0, and corresponds to the signal x of the input traffic of (i+1) a overlaid windows⁽ⁱ⁾ It is defined by following equation: x⁽ⁱ⁾=[x_ix_i+1...x_i+n-1]^T, and it is used for the measured value y of initial overlaid windows⁽⁰⁾By with lower section Formula definition: y⁽⁰⁾=A⁽⁰⁾x⁽⁰⁾。

17. a kind of non-transitory computer-readable storage media, record has the computer for sensing streaming data thereon Program, the computer program include the algorithm for being able to carry out following operation:

Input traffic is recursively sampled at least partially by the following gradually overlaid windows that operates with:

Recursively sequence of the selection for the sensing matrix A of the overlaid windows in the input traffic, the sensing square The sequence of battle array A includes initial sensing matrix A⁽⁰⁾, sensing matrix A⁽ⁱ⁾With sensing matrix A⁽ⁱ⁺¹⁾, the institute of (i+2) a overlaid windows State sensing matrix A⁽ⁱ⁺¹⁾It is defined by following equation: A⁽ⁱ⁺¹⁾=[a₂ ⁽ⁱ⁾,a₃ ⁽ⁱ⁾,...,a_n ⁽ⁱ⁾,a_l ⁽ⁱ⁾], wherein a₁ ⁽ⁱ⁾、a₂ ⁽ⁱ⁾、a₃ ⁽ⁱ⁾... and a_n ⁽ⁱ⁾The respectively described sensing matrix A⁽ⁱ⁾The 1st, 2,3 ... and n arrange, n is the length of each overlaid windows, and i is big In or equal to 0；And

The measured value y for being used for (i+2) a overlaid windows is obtained using following equation⁽ⁱ⁺¹⁾: y⁽ⁱ⁺¹⁾=y⁽ⁱ⁾+(x_i+n- x_i)a_l ⁽ⁱ⁾, wherein i is greater than or equal to 0, and corresponds to the signal x of the input traffic of (i+1) a overlaid windows⁽ⁱ⁾ It is defined by following equation: x⁽ⁱ⁾=[x_ix_i+1...x_i+n-1]^T, and it is used for the measured value y of initial overlaid windows⁽⁰⁾By with lower section Formula definition: y⁽⁰⁾=A⁽⁰⁾x⁽⁰⁾。

18. a kind of equipment for executing the compression sensing of streaming data comprising:

Memory is configured to store the data from input pickup data flow；And

Processor is configured to:

Input pickup data flow is recursively sampled at least partially by the following overlaid windows that operates with gradually:

Recursively sequence of the selection for the sensing matrix A of the overlaid windows in the input pickup data flow, it is described The sequence for sensing matrix A includes initial sensing matrix A⁽⁰⁾, sensing matrix A⁽ⁱ⁾With sensing matrix A⁽ⁱ⁺¹⁾, (i+2) a overlapping window The sensing matrix A of mouth⁽ⁱ⁺¹⁾It is defined by following equation: A⁽ⁱ⁺¹⁾=[a₂ ⁽ⁱ⁾,a₃ ⁽ⁱ⁾,...,a_n ⁽ⁱ⁾,a_l ⁽ⁱ⁾], wherein a₁ ⁽ⁱ⁾、 a₂ ⁽ⁱ⁾、a₃ ⁽ⁱ⁾... and a_n ⁽ⁱ⁾The respectively described sensing matrix A⁽ⁱ⁾The 1st, 2,3 ... and n arrange, n be each overlaid windows length, And i is greater than or equal to 0；And

The measured value y for being used for (i+2) a overlaid windows is obtained using following equation⁽ⁱ⁺¹⁾: y⁽ⁱ⁺¹⁾=y⁽ⁱ⁾+(x_i+n- x_i)a_l ⁽ⁱ⁾, wherein i is greater than or equal to 0, and corresponds to the input pickup data flow of (i+1) a overlaid windows Signal x⁽ⁱ⁾It is defined by following equation: x⁽ⁱ⁾=[x_ix_i+1...x_i+n-1]^T, and it is used for the measured value y of initial overlaid windows⁽⁰⁾It is defined by following equation: y⁽⁰⁾=A⁽⁰⁾x⁽⁰⁾。

19. the equipment according to claim 18 for executing the compression sensing of streaming data, wherein the processing Device is configured to carry out recurrence sampling based on the recursive scheme for executing the sensing.

20. the equipment according to claim 18 for executing the compression sensing of streaming data, wherein the processing Device is further configured in the feelings for the matrix multiple for not executing any one of sequence for being related to sensing matrix A sensing matrix The measured value y is obtained under condition⁽ⁱ⁺¹⁾。

21. the equipment according to claim 20 for executing the compression sensing of streaming data, further comprises For transmitting previously having estimated about obtained during previous estimated values obtain step about the input pickup data flow The memory of the input information of evaluation.

22. the equipment according to claim 20 for executing the compression sensing of streaming data, wherein the processing Device is further configured to be executed based on information obtained during data flow support detecting step and count estimation.

23. the equipment according to claim 20 for executing the compression sensing of streaming data, wherein the processing Device is further configured to be calculated for data flow support set most based on data obtained during recursive estimation step Small two multiply estimation LSE value.

24. the equipment according to claim 23 for executing the compression sensing of streaming data, wherein the processing Device is further configured to calculate the least-squares estimation value being computed, counting estimated value and be walked in previous estimated values The average value of rapid period previous estimated values obtained.

25. the equipment according to claim 24 for executing the compression sensing of streaming data, wherein the processing Device, which is further configured, asks flat with the degree of error to the method and step for sensing streaming data executed by the equipment Mean value.

26. the equipment according to claim 18 for executing the compression sensing of streaming data, wherein the processing Device is further configured to average to the signal estimated value obtained from the gradually overlaid windows.

27. the equipment according to claim 18 for executing the compression sensing of streaming data, further comprises It is configured to measure one or more sensors of the input pickup data flow.